The value of $${\left( {\frac{{1 - \cot \theta }}{{1 - \tan \theta }}} \right)^2} + 1,$$ 0° < θ < 90°, is equal to:
A. cosec2θ
B. sin2θ
C. cos2θ
D. sec2θ
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\left( {\frac{{1 - \cot \theta }}{{1 - \tan \theta }}} \right)^2} + 1 \cr & = {\left( {\frac{{1 - \frac{{\cos \theta }}{{\sin \theta }}}}{{1 + \frac{{\sin \theta }}{{\cos \theta }}}}} \right)^2} + 1 \cr & = {\left( {\frac{{\sin \theta - \cos \theta }}{{\sin \theta }} \times \frac{{\cos \theta }}{{\cos \theta - \sin \theta }}} \right)^2} + 1 \cr & = {\left( {\frac{{\sin \theta - \cos \theta \times \cos \theta }}{{ - \sin \theta \left( {\sin \theta - \cos \theta } \right)}}} \right)^2} + 1 \cr & = {\left( {\frac{{ - \cos \theta }}{{\sin \theta }}} \right)^2} + 1 \cr & = {\cot ^2}\theta + 1 \cr & = {\text{cose}}{{\text{c}}^2}\theta \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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